Interest in mass analysis of multiply charged ions has mushroomed since the demonstration a few years ago that they could be readily produced by so-called Electrospray (ES) Ionization from large, complex and labile molecules in solution. This development has been described in several U.S. Pat. Nos. (Labowsky et al., 4,531,056; Yamashita et al., 4,542,293; Henion et.al. 4,861,988; and Smith et al. 4,842,701 and 4,887,706) and in several recent review articles [Fenn et al., Science 246, 64 (1989); Fenn et al., Mass Spectrometry Reviews 6, 37 (1990); Smith et al., Analytical Chemistry 2, 882 (1990]. Because of extensive multiple charging ES ions of large molecules almost always have mass/charge (m/z) ratios of less than about 2500 so they can be weighed with relatively simple and inexpensive conventional analyzers. Intact ions of polar species such as proteins and other biopolymers with molecular weights (Mr's) of 200,000 or more have been produced. ES ions have been produced from polyethylene glycols with Mr's up to 5,000,000. Because such ions have as many as 4000 charges they can be "weighed" with quadrupole mass filters having an upper limit for m/z of 1500! [T. Nohmi et al., J. Am. Chem. Soc. 114, 3241 (1992)].
ES ions always comprise species that are themselves anions or cations in solution, or are polar molecules to which solute anions or cations are attached by ion-dipole forces. While attachment of charge is the prevalent mode of ion formation, ionization may also occur in a "deduct" mode. In other words, a molecule may be charged by the loss of charged mass. For example, a neutral molecule may become negatively charged by losing a proton with each charge. The term "adduct ion" will be used here to refer to both modes of ion formation. For species large enough to produce ions with multiple charges, the mass spectra always comprise sequences of peaks. The sequence for any particular species is coherent in the sense that the ions of each peak differ only by one charge from those of the nearest peak of the same species (on either side). As discussed by Mann et.al.[(Anal. Chem. 61, 1702 (1989)]such coherence and multiplicity lead to improved precision in the determination of Mr because each peak constitutes an independent measure of the parent ion mass. Averaging over the m/z values of several peaks can substantially reduce random errors, thereby significantly increasing the confidence in, and precision of, mass assignments. However, such averaging has no affect on systematic errors, e.g. those due to errors in the calibration of the instrument mass scale. Thus, although peak multiplicity does make possible an increase in the precision of an Mr determination it does not necessarily provide an increase in its accuracy.
As mentioned above, the potential of peak multiplicity to improve the precision of mass assignment was first recognized by Mann et al. (11) They noted that there are three unknowns associated with the ions of a particular peak: the molecular weight Mr of the parent species, the number i of charges on the ion, and the mass ma of each adduct charge. Therefore, mass/charge (m/z) values for the ions of any three peaks of the same parent species would fix the values of each unknown. However, there is a relation between the peaks such that they form a coherent sequence in which the number of charges i varies by one from peak to peak. Consequently, the m/z values of any pair of peaks are sufficient to fix Mr for the parent species, provided that the masses of the adduct charges are the same for all ions of all the peaks in the sequence. Mann et.al. also described procedures for optimum averaging of the set of Mr values from the m/z values of the possible peak pairings. In addition, they introduced a somewhat different approach by which the measured spectrum with its sequence of peaks for a particular parent species could be transformed into the spectrum that would have been obtained if all the ions of the parent species had had a single massless charge. This single peak, obtained by deconvoluting the measured spectrum, reflects the sum of contributions from all the ions of that parent species, no matter what their charge state. Moreover, because random contributions are not similarly summed, the signal/noise ratio in the transformed spectrum is greater than in the original measured spectrum. The deconvolution procedure can be carried out by direct computer processing of the raw data from the mass spectrometer. Moreover, it can extract an Mr value for each species in a mixture by taking advantage of the coherence in the m/z values for the ions of a particular species. Such resolution of mixtures can be enhanced by so-called "entropy-based" computational procedures described, for example, in a recent paper by Reinhold and Reinhold [J. Am. Scc. Mass Spectrom. 3, 207 (1992)]. Indeed, resolution can be achieved even when some of the ions of different species have almost the same apparent m/z values. i.e. when some of the peaks in the measured spectrum comprise almost-exact superpositions of two or more peaks for ions of different species.
In spite of the effectiveness of this deconvolution procedure as originally described, and in spite of improvements that have since been incorporated by various users, it suffers from some disadvantages. It requires an a priori assumption that the mass of each adduct charge is the same for all ions of a particular species as well as an assumption of a particular value for that mass. If either of these assumptions is faulty, the resulting value of Mr for the parent species may be incorrect. Moreover, even if the assumptions are correct they neither eliminate nor reveal any errors due to faulty calibration of the analyzer's m/z scale. Nor does the deconvoluted spectrum provide any information on the magnitude or direction of the possible error.